In this article, some methodological statements of the formation of mathematical models in the problems of machine dynamics are elucidated. The presence of a cushioned freight in the form of the fastened vehicle complicates the system, so that the equations describing its oscillations are too complicated and unsuitable for practical usage. It is shown that with all the complexity of the research object, it is expedient to form the mathematical model at the level of the design diagram (model) with a relatively small number of degrees of freedom. The peculiarities of mathematical modelling of the motion processes of specialized articulated vehicles for transportation of cars, namely, formation of the design diagram (model), making the necessary assumptions, choosing the independent coordinates and writing down the second-order Lagrange equations describing the system oscillations, are presented. While modelling, the most typical case, namely, the motion over the unit prominence (road shock), the effect of which on the wheels of the articulated vehicle is of the impact type, is considered. The choosing of the initial perturbation in the form of a unit impact is caused by the possibility of obtaining an impact characteristic, which is defined as the reaction of the system on the δ-function. In addition, under the impact action, it is possible to carry out the direct visual analysis of non-interfered single-frequency oscillatory processes, which allows to quickly obtain the approximate express-evaluation of the amplitude values of the process, frequencies of oscillations, as well as the oscillations damping decrement of the two-section articulated vehicle, if it is necessary.

The mathematical model of the articulated vehicle consisting of a tractor and a semi-trailer in the form of a linear system having 9 degrees of freedom is developed. It consists of three cushioned masses, namely, the frame of the truck tractor, the frame of the semi-trailer and three non-cushioned masses, which are axles with wheels as an assembly. Both sections of this system are connected by the saddle-coupling element that is not absolutely rigid. While moving, the frames of the truck tractor and of the semi-trailer performs oscillatory motion in the vertical plane and angular oscillations about an axis passing through the centre of masses. The axles with wheels in the assembly oscillate only in the vertical plane. The peculiarity of the model is that the elastic and damping properties of the suspension of vehicle fixed on the semi-trailer are taken into account. The solution of the mathematical model allows to obtain the impact characteristic, to calculate the amplitude-frequency characteristic and to obtain the required (unknown) values of the root-meansquare accelerations of the non-cushioned masses.

The technology of systemic consideration of the problems of formation of mathematical models in the form of block diagrams (structure charts) which are equivalent in dynamic relation to the systems of automatic control is offered.